JEE MATHEMATICS MCQ: 3D GEOMETRY SYSTEM

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Analyzing +4 | -1

A B C D

is a tetrahedron such that each

\triangle A B C, \triangle A B D

and

\triangle A C D

has a right angle at

A

. If

\operatorname{ar}(\triangle A B C)=k_1

\operatorname{ar}(\triangle A B D)=k_2, \operatorname{ar}(\triangle B C D)=k_3

, then

\operatorname{ar}(\triangle A C D)

View answer and explanation

Correct option: C

\sqrt{\left|k_1^2+k_2^2-k_3^2\right|}

The correct answer is C (12) because it is the value of 6(a+b+c) after finding the relationship between a, b, and c from the coplanarity conditions.

More Questions from 3D GEOMETRY SYSTEM

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\left( { - 10,\;8} \right)

\left( { - 6,\;12} \right)

\left( {4,\; - 2} \right)

\left( { - 2,\;4} \right)

y z

(1,-2,4)

(3,-4

5)

p

2 x+y-3=0

3 x-y-2=0

x-p y+5=0

O\left( {0,0} \right),A\left( {a,0} \right)

B\left( {0,a} \right).

A(1,0,3)

B(4,7,1)

C(3,5,3)

\frac{x}{1}=\frac{y}{2}=\frac{z}{3}, \frac{x}{2}=\frac{y}{1}=\frac{z}{3}

\frac{x-1}{1}=\frac{2-y}{2}, z=3